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The notion of tamed Dirichlet space by distributional lower Ricci curvaturebounds was proposed by Erbar, Rigoni, Sturm and Tamanini as the Dirichlet spacehaving a weak form of Bakry-\'Emery curvature lower bounds in distributionsense. In this framework, we establish the Littlewood-Paley-Stein inequalityfor $L^p$-functions and $L^p$-boundedness of $q$-Riesz transforms with $q>1$,which partially generalizes the result by Kawabi-Miyokawa.

The Littlewood-Paley-Stein inequality for Dirichlet space tamed by distributional curvature lower bounds